The graph below shows the curve y = k (2x) + c, where k and c are constants. Find the values of c and k.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. The value of a car decreases each year. This value can be calculated using the function

P(t) = 32 000rt where P(t) is the value of the car in USD, t is the number of years after it was first bought t  0 and r is a constant 0  r  1.

(a) (i) Write down the value of the car when it was first bought.

(ii) One year later the value of the car was 27 200 USD. Find the value of r.

(b) Find how many years it will take for the value of the car to be less than 8000 USD

 

2. The graph below shows the curve y = k (2x) + c, where k and c are constants. Find the values of c and k.

3. The illustration below shows a rope between two clips A and B. The points A and B are at equal heights above the ground. P is the lowest point on the rope. The floor is represented by the x-axis. The x- coordinate of A is –2 and the x-coordinate of B is 2. Point P is on the y-axis. The shape of the rope is

given by y = 2x + 2–x where –2 ≤ x ≤ 2. A

a) Find the coordinate point A.

b) Find the coordinate point B.

c) Calculate the height of the point P.

d) Find the range of y. inequality symbols.

 

4. The function 𝑓(𝑥) = 𝑝 ∙ 0.4𝑥 + 𝑞 is such that 𝑓(−1) = 15.25 and 𝑓(1) = 4.12

 

a) Find the value of p.

b) Find the value of q.

c) Find the y –intercept

d) State the equation of the horizontal asymptote, if any.

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